Hodge was the biggest contributor to the Royals’ competitive total of 164-5 with Ashok Maneria adding an invaluable 40.
Manoj Tiwary fought a lone battle and scored 59 off 49 balls as Knight Riders were restricted to 142-9.
Knight Riders were forced to play a catch-up game after Singh removed Jacques Kallis and captain Gautum Gambhir off successive deliveries and leftarm spinner Ankeet Chavan made it 8-3 by having Brendon McCullum plumb leg before wicket.
It was the Royals’ second successive win, having beaten Kings XI Punjab in the first match.